DocumentCode :
938760
Title :
Weak convergence and asymptotic properties of adaptive filters with constant gains
Author :
Kushner, Harold J. ; Shwartz, Adam
Volume :
30
Issue :
2
fYear :
1984
fDate :
3/1/1984 12:00:00 AM
Firstpage :
177
Lastpage :
182
Abstract :
The basic adaptive filtering algorithm 
is analyzed using the theory of weak convergence. Apart from some very special cases, the analysis is hard when done for each fixed 
. But the weak convergence techniques are set up to provide much information for small 
. The relevant facts from the theory are given. Define 
by 
on 
. Then weak (distributional) convergence of 
and of 
is proved under very weak assumptions, where 
as 
. The normalized errors 
are analyzed, where 
is a "stable" point for the "mean" algorithm. The asymptotic properties of a projection algorithm are developed, where the 
are truncated at each iteration, if they fall outside of a given set.
is analyzed using the theory of weak convergence. Apart from some very special cases, the analysis is hard when done for each fixed . But the weak convergence techniques are set up to provide much information for small . The relevant facts from the theory are given. Define by on . Then weak (distributional) convergence of and of is proved under very weak assumptions, where as . The normalized errors are analyzed, where is a "stable" point for the "mean" algorithm. The asymptotic properties of a projection algorithm are developed, where the are truncated at each iteration, if they fall outside of a given set.Keywords :
Adaptive filters; Adaptive filters; Algorithm design and analysis; Convergence; Differential equations; Filtering algorithms; Filtering theory; Information analysis; Mathematics; Projection algorithms; Random variables;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1984.1056897
Filename :
1056897
Link To Document :
